Whatever troubles Jeremy Corbyn might have elsewhere, there is one place where he is unambiguously winning: Facebook. His personal page has more than 770,000 “Likes” and even more users will see its content shared by friends, or suggested underneath other articles. In a space where attention is currency, this is a huge achievement. In the week that Theresa May became Prime Minister, Corbyn’s Facebook page reached a third of all UK internet users, according to a source inside Labour’s digital team.

The amplifying – and so potentially distorting – effect of Facebook on public discourse is poorly understood, but it cannot be ignored. The social networking site’s influence, size and revenue are unmatched: while Twitter has 310 million monthly active users, Facebook has 1.65 billion. Two-thirds of Britons use it every month.

The media are waking up to the reality that Facebook is both a conduit for their stories and a rival for their money. Politicians face a similar challenge but their trade-off is this: they get a direct connection to activists and supporters but with the risk of creating insular, self-reinforcing communities. (On the Jeremy Corbyn Facebook page, no one can hear you scream “unelectable”.)

We talk about the “Westminster bubble” but we should talk about the “Facebook bubble”, too. Most of us make friends who are like us in background and political leanings. Facebook’s algorithms give us more of what we have already shown we like. This creates increasingly polarised communities without us even noticing. Unlike when you walk into a petrol station and see the Sun next to the Guardian, on the internet it’s easy to forget that other opinions are possible.

There is another problem that is shared by news media and political parties. “Online, people like people,” is how one campaigner put it to me. Just as star columnists command big money, we have seen a wave of politicians (including Donald Trump and Bernie Sanders in the US) whose personal followings cannot be neatly merged with existing members who believe that “the party” transcends any particular leader. “Bernie has blood on his hands,” read a typical comment on one Sanders Facebook page after the senator backed Hillary Clinton.

Thanks to Facebook and the campaign group Momentum, personal supporters of Corbyn have flooded into Labour. His Facebook page has 250,000 more Likes than the Labour Party page, which recently passed the half-million mark. (Angela Eagle’s page has around 18,900 and Owen Smith’s 6,600.) It is a measure of Corbyn’s online success that only 51 per cent of those who were full members at the last election think he is doing a good job. However, he has reshaped the party in his own image, and it now has a pro-Corbyn majority.

How parties deal with this personal style of politics is anyone’s guess. The Tories perhaps do it best: by selecting only two leadership candidates to go to the membership, they ensure that direct democracy is tempered by the parliamentary party.

The “Facebookification” of politics is not all negative. An engaged local MP can create a page for his or her constituency that can bring together thousands of citizens who care passionately about the area. Using online media also helps parties to connect with voters once considered hard to reach, such as young people and those living outside cities. Yet there are downsides, which are scarier because they are largely invisible. The ethnic targeting of adverts that we saw in the London mayoral campaign is easier online, where social networks know almost everything about you. For example, it would be possible to target an anti-immigration message at those in majority-white areas.

Then there is what the behavioural economist Cass Sunstein calls “group polarisation theory”. In closed communities, the louder, more extreme voices dominate; moderates leave; those who remain fall into step with the prevailing direction. That’s how you end up with unofficial Corbyn-supporting pages on which words such as “Zio” (short for “Zionist” and proscribed by Shami Chakrabarti’s review into anti-Semitism in the party) are bandied about, or forums on which suggesting any potential accommodation with the wider electorate on welfare or immigration will have you labelled a “Blairite”, “Tory-lite” or, simply, “traitor”.

Wrapped in with this is a hatred and suspicion of the mainstream media, or “MSM”. Just as Boris Johnson, an Old Etonian, led a revolt against “the elites” during the referendum campaign, so many online media organisations prosper by promising to reveal “what the media won’t tell you”.

There are independent left-wing sites such as the Canary that are as briskly biased in favour of Corbyn as the Sun is biased against him, and get almost all of their traffic from Facebook. Quite often, I find that I am bombarded with the same attack line or conspiracy theory – that “Blairites” didn’t oppose George Osborne’s welfare cuts, say, or that Angela Eagle staged an attack on her constituency office as a “false flag” – and find that it originated on a popular pro-Corbyn Facebook page.

There is no regulation of these spaces. The law cannot touch them and, for many, they are more trusted as a source of news than the “MSM”. They are encouraging an anti-elite, anti-expert, anti-media populist tone in politics. To begin to tackle this, we should acknowledge just how powerful Facebook has become. “Facebook has a responsibility to society beyond servicing shareholders, Wall Street and VC investors,” says Emily Bell, the director of the Tow Centre for Digital Journalism at Columbia University, New York. “Just as a water company has a duty not to poison the supply, so Facebook has a responsibility to use its significant distribution power for better democratic and civic outcomes.”

Update, 27 March: This article originally referred to Jeremy Corbyn losing if the leadership election had the same selectorate as last year. However, that's too strong a conclusion to draw from the YouGov data so I've amended it to reflect the broader point about weakening support from full members.

Labour’s renationalisation plans look nothing like the 1970s

A community energy company in Nottingham, a credit union in Oldham and, yes, Britain's most popular purveyor of wine coolers. No, this is not another diatribe about about consumer rip-offs. Quite the opposite – this esoteric range of innovative companies represent just a few of those which have come to the attention of the Labour leadership as they plot how to turn the abstract of one of their most popular ideas into a living, neo-liberal-shattering reality.

I am talking about nationalisation – or, more broadly, public ownership, which was the subject of a special conference this month staged by a Labour Party which has pledged to take back control of energy, water, rail and mail.

The form of nationalisation being talked about today at the top of the Labour Party looks very different to the model of state-owned and state-run services that existed in the 1970s, and the accompanying memories of delayed trains, leaves on the line and British rail fruitcake that was as hard as stone.

In John McDonnell and Jeremy Corbyn’s conference on "alternative models of ownership", the three firms mentioned were Robin Hood Energy in Nottingham, Oldham credit union and, of course, John Lewis. Each represents a different model of public ownership – as, of course, does the straightforward takeover of the East Coast rail line by the Labour government when National Express handed back the franchise in 2009.

Robin Hood is the first not-for-profit energy company set up a by a local authority in 70 years. It was created by Nottingham city council and counts Corbyn himself among its customers. It embodies the "municipal socialism" which innovative local politicians are delivering in an age of austerity and its tariffs delivers annual bills of £1,000 or slightly less for a typical household.

Credit unions share many of the values of community companies, even though they operate in a different manner, and are owned entirely by their customers, who are all members. The credit union model has been championed by Labour MPs for decades.

Since the financial crisis, credit unions have worked with local authorities, and their supporters see them as ethical alternatives to the scourge of payday loans. The Oldham credit union, highlighted by McDonnell in a speech to councillors in 2016, offers loans from £50 upwards, no set-up costs and typically charges interest of around £75 on a £250 loan repaid over 18 months.

Credit unions have been transformed from what was once seen as a "poor man's bank" to serious and tech-savvy lenders where profits are still returned to customers as dividends.

Then there is John Lewis. The "never-knowingly undersold" department store is owned by its 84,000 staff, or "partners". The Tories have long cooed over its pledge to be a "successful business powered by its people and principles" while Labour approves of its policy of doling out bonuses to ordinary staff, rather than just those at the top. Last year John Lewis awarded a partnership bonus of £89.4m to its staff, which trade website Employee Benefits judged as worth more than three weeks' pay per person (although still less than previous top-ups).

To those of us on the left, it is a painful irony that when John Lewis finally made an entry into politics himself – in the shape of former managing director Andy Street – it was to seize the Birmingham mayoralty ahead of Labour's Sion Simon last year. (John Lewis the company remains apolitical.)

Another model attracting interest is Transport for London, currently controlled by Labour mayor Sadiq Khan. TfL may be a unique structure, but nevertheless trains feature heavily in the thinking of shadow ministers, whether Corbynista or soft left. They know that rail represents their best chance of quick nationalisation with public support, and have begun to spell out how it could be delivered.

Yes, the rhetoric is blunt, promising to take back control of our lines, but the plan is far more gradual. Rather than risk the cost and litigation of passing a law to cancel existing franchises, Labour would ask the Department for Transport to simply bring routes back in-house as each of the private sector deals expires over the next decade.

If Corbyn were to be a single-term prime minister, then a public-owned rail system would be one of the legacies he craves.

His scathing verdict on the health of privatised industries is well known but this month he put the case for the opposite when he addressed the Conference on Alternative Models of Ownership. Profits extracted from public services have been used to "line the pockets of shareholders" he declared. Services are better run when they are controlled by customers and workers, he added. "It is those people not share price speculators who are the real experts."

It is telling, however, that Labour's radical election manifesto did not mention nationalisation once. The phrase "public ownership" is used 10 times though. Perhaps it is a sign that while the leadership may have dumped New Labour "spin", it is not averse to softening its rhetoric when necessary.

So don't look to the past when considering what nationalisation and taking back control of public services might mean if Corbyn made it to Downing Street. The economic models of the 1970s are no more likely to make a comeback then the culinary trends for Blue Nun and creme brûlée.

Instead, if you want to know what public ownership might look like, then cast your gaze to Nottingham, Oldham and dozens more community companies around our country.

Peter Edwards was press secretary to a shadow chancellor, editor of LabourList and a parliamentary candidate in 2015 and 2017.